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Abstract Making use of a mixed variational formulation including the Green function of the substrate, a finite element model is derived for the static analysis of Timoshenko beams in bilateral frictionless contact with an elastic half-space. Numerical results are obtained by adopting locking-free Hermite polynomials for the Timoshenko beam and piecewise constant reaction over the soil. Foundation beams loaded by forces and couples at the midspan illustrate accuracy and convergence properties of the proposed formulation. [ABSTRACT FROM AUTHOR]

Interface displacements, surface tractions and stresses of a flexible beam bonded to an elastic orthotropic half-plane are analysed by means of a Finite Element-Boundary Integral Equation (FE-BIE) method. Numerical results are obtained by using locking-free shear deformable beams and piecewise constant interfacial reactions. Making use of the generalised Green's function for the half-plane, the mechanical behaviour of fully bonded or detached beams subjected to force, couple or thermal load is investigated. The special cases of a beam in bilateral frictionless contact with the half-plane and a beam having a vanishing bending rigidity (thin film) are considered also. In particular, the maximum bending moment of beams subjected to a vertical point force are compared with some closed-form solutions of the contact problem of a rigid indenter and with the solution of an infinite Euler–Bernoulli beam in bilateral frictionless contact with an isotropic substrate. [ABSTRACT FROM AUTHOR]

Saint-Venant decay rate of end effects is investigated for generally laminated orthotropic strips under self-equilibrated end loads. The problem is governed by a fourth-order partial differential equation for the Airy stress function with discontinuous coefficients at the layer interfaces, where displacements and traction continuities are imposed. The solution is found in the form of product of an exponentially decaying function along the strip and an unknown function defined over its total height. External face and interface conditions are used to obtain the characteristic equation for the eigenvalues governing the decay rate of end effects along the strip. For orthotropic and strongly orthotropic sandwich strips the transcendental eigenvalue equation is explicitly given. The case of laminated strips with periodic layout is finally considered. Making use of the homogenization method, both effective elastic constants and expressions for the local stress variation at the layer level are obtained. Numerical calculations confirm that the eigenvalues of the homogenized material are the asymptotic values of those of periodically laminated strips when the number of layers increases. Moreover, homogenization method is shown to be very powerful also in the calculation of local stress distributions.

This paper presents a displacement-based model for orthotropic beams under plane linear elasticity based on the only kinematic assumption of transverse inextensibility. Any given axial and transverse loading as well as boundary conditions at the beam ends are considered. The solution is decomposed into the principal and the residual part (corresponding to the interior and the boundary problems) which are obtained by series expansions of polynomial functions and eigenfunctions, respectively. It is proved that the proposed one-dimensional theory gives both interior and boundary exact two-dimensional elasticity solutions for strongly orthotropic materials, i.e. for ratio between shear modulus and axial Young modulus approaching zero. For isotropic and orthotropic materials the accuracy of the beam model is also analysed and compared with that of other theories. In particular, the complementary energy error of the interior solution with respect to two-dimensional elasticity is evaluated, the asymptotic estimate of the characteristic decay length of end effects given in Choi and Horgan [J. Appl. Mech. ASME, 44, 424–430 (1977)] by two-dimensional analysis is reobtained and the range of validity of boundary solution is discussed. The numerical results presented agree very well with exact and finite element solutions even in the neighbourhood of clamped cross-sections, where the solution is mainly governed by the boundary problem.

A Finite Element-Boundary Integral Equation (FE-BIE) coupling method is proposed to investigate a flexible bar weakly attached to an elastic orthotropic half-plane. Firstly, the analysis focused on the case of a bar subjected to horizontal forces and thermal loads considering interfacial displacements linearly proportional to the tangential traction. Secondly, the debonding behaviour of a composite reinforcement glued to a substrate has been modelled. Using an incremental nonlinear analysis, a bilinear elastic-softening interfacial traction-slip law has been implemented simulating the delamination of pure mode II. Finally, the influence of the anchorage length on the ultimate bearing capacity of the adhesive joint has been investigated. [ABSTRACT FROM AUTHOR]